A261388 a(n) is the length of the longest stretch of consecutive primitive roots of the multiplicative group modulo prime(n).

1, 1, 2, 1, 3, 2, 3, 3, 3, 2, 3, 4, 3, 3, 4, 5, 5, 2, 3, 3, 3, 3, 7, 6, 5, 4, 5, 6, 4, 3, 4, 4, 5, 4, 6, 4, 4, 4, 6, 5, 6, 3, 5, 4, 5, 3, 4, 5, 7, 4, 7, 6, 4, 5, 6, 7, 9, 4, 4, 4, 9, 5, 4, 5, 4, 6, 4, 3, 8, 6, 7, 8, 5, 5, 4, 8, 5, 3, 5, 7, 8, 6, 6, 4, 4, 6, 9, 5, 4, 4, 11, 11, 5, 5, 5, 8, 7, 5, 6

Offset: 1

Author

Joerg Arndt, Aug 17 2015

Keywords

• nonn

Links

• Joerg Arndt, Table of n, a(n) for n = 1..9592 (terms for all primes < 10^5)

Crossrefs

Cf. A261438 (primes corresponding to records).

Programs

Mathematica

a[n_] := 1 + Max[ Join[{0}, Length/@ Select[ Split@ Differences @ PrimitiveRootList @ Prime @ n, #[[1]] == 1 &]]]; Array[a, 99] (* Giovanni Resta, Aug 17 2015 *)

PARI

consec_pr(p)= \\ max number of consecutive primroots
{
    my( v = vector(p-1) );
    my (g = znprimroot(p) );
    for (j=1, p-1,  if (gcd(p-1,j)==1, v[lift(g^j)]=1 ) );
    my ( m=0, t=0 );
    for (j=1, p-1, if ( v[j]==0, t=0 , t+=1; if ( t>m, m=t ); ); );
    return(m);
}
forprime(p=2,10^3, c=consec_pr(p);  print1( c,", " ); );